I want to know why don't we see a change in the position of stars during the night while we do see a change in the position of the moon. I've checked other online sources and some answers say that it is because they are too far away, is this true?

I mean for example if i'm laying down on the earth since sunset looking at the stars, and let's say I'm close to the equator, no matter the distance, I'll be looking at the stars and earth will turn about 180° until sunrise, so my angle of view will be about 180°.

Why not just look up for more than twenty minutes. You will see the stars move. Or if you don't have the patience, use a long exposure on your camera and look at the lovely arcs, as @Tildal shows.
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Rory AlsopJan 26 '14 at 20:16

This question appears to be off-topic because it is based on amazingly incorrect symptoms which the op could learn himself if he actually looked up.
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Rory AlsopJan 26 '14 at 20:17

@Rory: i guess i'll try a long exposure pic using my nikon, thanks for the idea
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Jihed JaouabiJan 26 '14 at 23:02

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It's a valid question, the fact that he is wrong in what he thinks doesn't make it less so. It is because he doesn't know that stars do move that he asks, so the answer, as @TildalWave did, explains so.
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Eduardo SerraJan 26 '14 at 23:11

I didn't want to speculate for the reasons of OP's false assumptions in my answer, there's simply too many possibilities, but one that's fairly common is that we tend to be predictable and periodic at that too, so we'd look at the night sky at more or less same times each night. Meaning that stars would be, on a daily basis (but not year long), more or less at the same position. This reminds me of a similar reason why Mercury was long assumed to be tidally locked with the Sun, since it's in 3:2 spin-orbital resonance with Earth and we always observed it facing the same side relative to Earth.
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TildalWaveJan 26 '14 at 23:22

2 Answers
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This is referred to as diurnal motion, due to Earth's rotation on its axis, and it affects apparent motion of stars differently depending on their position on the skies relative to the axis of Earth's rotation. For example, on northern hemisphere, the star that appears not to move at all is positioned so that the earth's axis of rotation points directly towards it, and is called a Polaris due to its role as a pole star. Stars further away from true north (not to be confused with magnetic north), will appear to prescribe a circle around it as the Earth completes one rotation on its axis:

A long exposure photograph of the night skies, showing their apparent motion

So what you assert, that the stars don't seem to move isn't exactly true. Stars closer to celestial equator will move at equal apparent radial velocity as any object fixed on the night skies would (so at the speed of Earth's rotation), while the stars closer to celestial poles, while maintaining this radial velocity, will prescribe a smaller circle and appear to be more stationary. And the stars exactly aligned with the Earth's axis (like Polaris, but there isn't any such exact counterpart on the southern hemisphere), would appear not to move at all.

@KeithThompson So what you're saying is I am at most $0.2093472\dot2\ \%$ off in one small part of my answer on a question that used to conclude with a $100\ \%$ false assumption. If you don't mind, I won't edit that in then, it seems redundant...
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TildalWaveJan 29 '14 at 20:35

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Yes, that's what I'm saying (I'll take your word that the percentage is correct). You used the word "exactly", which happens to be incorrect. If I zoom in on your image, I think I can see Polaris showing a small arc. That doesn't affect your main point -- but I never said that it did, or that the inaccuracy is a huge deal. All I did was mention it.
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Keith ThompsonJan 29 '14 at 20:52

Well, it's pointing "exactly" at true north two times in one Earth's sidereal day, and it's off by a maximum of 0° 44' 21.9" otherwise. For a casual observer that isn't using stars for precision navigation, or is taking photographs with exposure shorter than at least a few minutes, it would appear stationary. By the amount the stars moved on that photo, you can see the exposure was close to 3 hours long. Here's one higher resolution photo of about 85 minute long exposure (well, 171 * 30 second long stacked frames at least).
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TildalWaveJan 29 '14 at 21:20

And changing "directly" to "almost directly" and "exactly aligned" to "almost exactly aligned" would have been more difficult than all that?
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Keith ThompsonJan 29 '14 at 21:28

As we view it, the moon moves westward across the sky due to the rotation of the earth, while at the same time it's moving eastward in its orbit at about 1 lunar diameter in about 57 minutes, or about 1 lunar diameter per hour or 12-14 degrees per day.

That's why the moon can be seen blocking out (or occulting) a bright star or planet as it slowly moves eastward in front of it for several minutes.

The actual motion of a star is too small to notice and it takes years to notice it without powerful telescopes. For general purpose, day-to-day astronomical observations, the actual motions of the stars in 3D space can be ignored.